數位簽章隨著電腦等運算設備的普及，已廣泛的應用到各個生活及職場領域，如 : IC 卡、智慧卡、RFID、數位現金、線上支付、行動商務、行動裝置身分驗證、文書軟體…等。而縮短數位簽章的技術愈趨受到重視，對於無線設備而言，減少通信傳輸的位元數以節省電力或增加通信成功率，對於人類在低頻寬通信或低計算能力系統中，可帶來一定的效益。Boneh等學者基於雙線性配對(Bilinear Pairing)率先提出短簽章後，開啟了各方學者連續多年的討論與研究，其中Tso 等學者提出的短簽章方案在計算量方面有著顯著的突破，但因僅考慮單一用戶的環境，未考慮在多用戶的情況下使用者公鑰有被偽造的可能，Chen 及Kong 等學者分別以不同的公鑰替換攻擊方式，破解了Tso 的短簽章方案。本篇論文改良了Tso 的短簽章方案，並在隨機預言機模型(Random Oracle Model)上驗證其安全性，證明此新的方案除了能有效防禦公鑰替換攻擊外，還能具備足夠的安全性。Digital Signature is getting popular along with the computing devices such as computers. It has been widely used in various fields of life and workplaces, such as IC cards, smart cards, RFID, digital cash, online payment, mobile commerce, mobile identity verification, document software …etc. And the technology of shortened digital signature is getting increasing attention. For wireless communication, it can bring certain benefits in the field of low bandwidth communication and low computing power system which reducing the number of bits transmitted by the communication to save power or increase the success rate of communications.Boneh and Lynn firstly proposed a short signature based on bilinear pairing. After this, many scholars started discussions and research for many years. Among them, the Tso’s short signature scheme had a good performance in computation. However, this scheme was only considered for a single user environment, not considered for the case of multi-user. Chen and Kong et al respectively proposed the attack modes with replacement of public keys to break Tso’s short signature scheme. In this paper, we improve Tso's short signature scheme and verifies its security in the Random Oracle Model. It proves that the new scheme not only can effectively resist the public-key replacement attack, but also has enough security.